Linearisation techniques and the dual algorithm for a class of mixed singular/continuous control problems in reinsurance. Part II: Numerical aspects

This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 473; p. 128655
Main Authors: Goreac, Dan, Li, Juan, Wang, Pangbo, Xu, Boxiang
Format: Journal Article
Language:English
Published: Elsevier Inc 15.07.2024
Subjects:
Capital injection
Dividends
Dual algorithm
Dual dynamic programming
Linear programming
Occupation measure
Reinsurance
Singular/continuous control
93-08
Dividends
65K15
Singular/continuous control
Dual dynamic programming
Linear programming
Capital injection
91G50
49M20
93E20
Reinsurance
65C30
49J40
49M29
65K10
Occupation measure
Dual algorithm
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the no-reinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations. •We provide a validation of the Dual Linear Programming algorithm by showcasing its performance on two benchmarks.•With a relatively modest order of moments (4), the relative errors are of at most 3%.•Leveraging this algorithm reveals significant enhancements in the expected dividends, advocating for capital injections.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2024.128655